Hidden scaling in the quantum Hall metal-insulator transition

Abstract

Scaling properties of the quantum Hall metal-insulator transition are severely affected by finite-size effects in small systems. Surprisingly, despite the narrow spatial range where probability structure functions exhibit multifractal scaling, we clearly verify the existence of extended self-similarity---a hidden infrared scaling phenomenon related to the peculiar form of the crossover at the onset of nonmultifractal behavior. As finite-size effects get stronger for structure functions with negative orders, the parabolic approximation for the multifractal spectrum loses accuracy. However, by means of an extended self-similarity analysis, an improved evaluation of the multifractal exponents is attained for negative orders too, rendering them consistent with previous results, which rely on computations performed for considerably larger systems.